FRACTALS FOR ELECTRONIC APPLICATIONS

Example: : Cantor Set
• The oldest, simplest, most famous fractal
1 We begin with the closed interval [0,1].
2 Now we remove the open interval (1/3,2/3);
leaving two closed intervals behind.
3 We repeat the procedure, removing
the "open middle third" of each
of these intervals
4 And continue infinitely.
• Fractal dimension:
D = log 2 / log 3 = 0.63…
• Uncountable points, zero length
August 18th, 2006
Fractals for electronic applications
Maciej J. Ogorzałek